Entanglements in Systems with Multiple Degrees of Freedom

TL;DR

This paper investigates the entanglement properties in systems with multiple degrees of freedom, revealing how spin-orbital interactions influence entanglement length and phase behavior, with implications for quantum phases and nucleon systems.

Contribution

It introduces a detailed analysis of entanglement in spin-orbital coupled systems, including the construction of maximally entangled bases and phase diagrams.

Findings

Entanglement length is larger in itinerant fermion systems with spin and orbit.

Entanglement correlates with quantum phases in strongly correlated systems.

Entanglement phase diagram aligns with magnetic and orbital phase diagrams.

Abstract

We present the entanglement properties of the spin-orbital coupling systems with multiple degrees of freedom. After constructing the maximally entangled spin-orbital basis of bipartite, we find that the quantum entanglement length in the noninteracting itinerant Fermion system with spin and orbit is considerably larger than that in the system with only spin. In the SU(2)$\otimes$SU(2) spin-orbital interacting system, the entanglement, expressed in terms of the spin-orbital correlation functions, clearly manifests the close relationship with the quantum phases in strongly correlated systems; and the entanglement phase diagram of the finite-size systems is in agreement with the magnetic and orbital phase diagram of the infinite systems. The application of the present theory on nucleon systems is suggested.